McEvoy, who won his first event since 2004 in the SSE Scottish Hydro Challenge at the start of the month, carded six birdies in an opening 66 on the 7,582-yard Green Eagle Golf Course in Hamburg.
It looked set to give the 38-year-old from Essex the outright lead until American Julian Suri birdied four of his last five holes to also finish six under, a shot ahead of defending champion Alex Levy, former Masters winner Charl Schwartzel, Stuart Manley and Chris Paisley.
Woodsome Hall’s Chris Hanson had just one blemish on his card and three birdies to lie joint 33rd on two-under-par 70.
Malton’s Simon Dyson is a shot further back despite accumulating four birdies, three bogeys in the space of four holes on the back nine holding him back.
Harrogate’s John Parry shot level-par 72, he, too, collecting four birdies and one bogey plus an ugly triple-bogey seven at the 10th.
Hull’s Richard Finch and Howley Hall’s Marcus Armitage both shot 73, the former with two birdies and three bogeys and Armitage with one more of each.
Joint leader McEvoy said: “I’m very pleased. At the start of the week (I thought) it’s not really my style of golf course, to be honest.
“It’s wet out there and I’m not the longest of hitters. I’m quite average on tour, but I did everything kind of right (yesterday). When I got myself in trouble I got out of it well.”